Factorization And Integrable Systems

Author : Israel Gohberg,Nenad Manojlovic,Antonio, F. dos Santos
Publisher : Birkhäuser
Page : 227 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880039

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Factorization and Integrable Systems by Israel Gohberg,Nenad Manojlovic,Antonio, F. dos Santos Pdf

This volume comprises the specially prepared lecture notes of a a Summer School on "Factorization and Integrable Systems" held in September 2000 at the University of Algarve in Portugal. The main aim of the school was to review the modern factorization theory and its application to classical and quantum integrable systems. The program consisted of a number of short courses given by leading experts in the field.

Author : Israel Gohberg,Nenad Manojlovic,António Ferreira dos Santos
Publisher : Birkhauser
Page : 218 pages
File Size : 48,5 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 0817669388

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Factorization and Integrable Systems by Israel Gohberg,Nenad Manojlovic,António Ferreira dos Santos Pdf

Author : Olivier Babelon,Denis Bernard,Michel Talon
Publisher : Cambridge University Press
Page : 616 pages
File Size : 52,5 Mb
Release : 2003-04-17
Category : Science
ISBN : 9781139436793

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Introduction to Classical Integrable Systems by Olivier Babelon,Denis Bernard,Michel Talon Pdf

A clear and pedagogical introduction to classical integrable systems and their applications. It synthesizes the different approaches to the subject, providing a set of interconnected methods for solving problems in mathematical physics. Each method is introduced and explained, before being applied to particular examples.

Author : Martin A. Guest
Publisher : OUP Oxford
Page : 336 pages
File Size : 42,7 Mb
Release : 2008-03-13
Category : Mathematics
ISBN : 9780191606960

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From Quantum Cohomology to Integrable Systems by Martin A. Guest Pdf

Quantum cohomology has its origins in symplectic geometry and algebraic geometry, but is deeply related to differential equations and integrable systems. This text explains what is behind the extraordinary success of quantum cohomology, leading to its connections with many existing areas of mathematics as well as its appearance in new areas such as mirror symmetry. Certain kinds of differential equations (or D-modules) provide the key links between quantum cohomology and traditional mathematics; these links are the main focus of the book, and quantum cohomology and other integrable PDEs such as the KdV equation and the harmonic map equation are discussed within this unified framework. Aimed at graduate students in mathematics who want to learn about quantum cohomology in a broad context, and theoretical physicists who are interested in the mathematical setting, the text assumes basic familiarity with differential equations and cohomology.

Author : Boris A. Kupershmidt
Publisher : World Scientific
Page : 402 pages
File Size : 46,7 Mb
Release : 1990
Category : Mathematics
ISBN : 9810203160

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Integrable and Superintegrable Systems by Boris A. Kupershmidt Pdf

Some of the most active practitioners in the field of integrable systems have been asked to describe what they think of as the problems and results which seem to be most interesting and important now and are likely to influence future directions. The papers in this collection, representing their authors' responses, offer a broad panorama of the subject as it enters the 1990's.

Author : Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita
Publisher : American Mathematical Soc.
Page : 344 pages
File Size : 48,9 Mb
Release : 2002
Category : Geometry, Differential
ISBN : 9780821829394

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Integrable Systems, Topology, and Physics by Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita Pdf

Ideas and techniques from the theory of integrable systems are playing an increasingly important role in geometry. Thanks to the development of tools from Lie theory, algebraic geometry, symplectic geometry, and topology, classical problems are investigated more systematically. New problems are also arising in mathematical physics. A major international conference was held at the University of Tokyo in July 2000. It brought together scientists in all of the areas influenced by integrable systems. This book is the second of three collections of expository and research articles. This volume focuses on topology and physics. The role of zero curvature equations outside of the traditional context of differential geometry has been recognized relatively recently, but it has been an extraordinarily productive one, and most of the articles in this volume make some reference to it. Symplectic geometry, Floer homology, twistor theory, quantum cohomology, and the structure of special equations of mathematical physics, such as the Toda field equations--all of these areas have gained from the integrable systems point of view and contributed to it. Many of the articles in this volume are written by prominent researchers and will serve as introductions to the topics. It is intended for graduate students and researchers interested in integrable systems and their relations to differential geometry, topology, algebraic geometry, and physics. The first volume from this conference also available from the AMS is Differential Geometry and Integrable Systems, Volume 308 CONM/308 in the Contemporary Mathematics series. The forthcoming third volume will be published by the Mathematical Society of Japan and will be available outside of Japan from the AMS in the Advanced Studies in Pure Mathematics series.

Author : Chaohao Gu,Anning Hu,Zixiang Zhou
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 48,8 Mb
Release : 2006-07-09
Category : Science
ISBN : 9781402030888

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Darboux Transformations in Integrable Systems by Chaohao Gu,Anning Hu,Zixiang Zhou Pdf

The Darboux transformation approach is one of the most effective methods for constructing explicit solutions of partial differential equations which are called integrable systems and play important roles in mechanics, physics and differential geometry. This book presents the Darboux transformations in matrix form and provides purely algebraic algorithms for constructing the explicit solutions. A basis for using symbolic computations to obtain the explicit exact solutions for many integrable systems is established. Moreover, the behavior of simple and multi-solutions, even in multi-dimensional cases, can be elucidated clearly. The method covers a series of important equations such as various kinds of AKNS systems in R1+n, harmonic maps from 2-dimensional manifolds, self-dual Yang-Mills fields and the generalizations to higher dimensional case, theory of line congruences in three dimensions or higher dimensional space etc. All these cases are explained in detail. This book contains many results that were obtained by the authors in the past few years. Audience: The book has been written for specialists, teachers and graduate students (or undergraduate students of higher grade) in mathematics and physics.

Author : Vladimir V Sokolov
Publisher : World Scientific
Page : 346 pages
File Size : 43,7 Mb
Release : 2020-06-05
Category : Science
ISBN : 9789811219665

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Algebraic Structures In Integrability: Foreword By Victor Kac by Vladimir V Sokolov Pdf

Relationships of the theory of integrable systems with various branches of mathematics are extremely deep and diverse. On the other hand, the most fundamental exactly integrable systems often have applications in theoretical physics. Therefore, many mathematicians and physicists are interested in integrable models.The book is intelligible to graduate and PhD students and can serve as an introduction to separate sections of the theory of classical integrable systems for scientists with algebraic inclinations. For the young, the book can serve as a starting point in the study of various aspects of integrability, while professional algebraists will be able to use some examples of algebraic structures, which appear in the theory of integrable systems, for wide-ranging generalizations.The statements are formulated in the simplest possible form. However, some ways of generalization are indicated. In the proofs, only essential points are mentioned, while for technical details, references are provided. The focus is on carefully selected examples. In addition, the book proposes many unsolved problems of various levels of complexity. A deeper understanding of every chapter of the book may require the study of more rigorous and specialized literature.

Author : Martin Ulrich Schmidt
Publisher : American Mathematical Soc.
Page : 111 pages
File Size : 50,8 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804605

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Integrable Systems and Riemann Surfaces of Infinite Genus by Martin Ulrich Schmidt Pdf

This memoir develops the spectral theory of the Lax operators of nonlinear Schrodinger-like partial differential equations with periodic boundary conditions. Their spectral curves, i.e., the common spectrum with the periodic shifts, are generically Riemann surfaces of infinite genus. The points corresponding to infinite energy are added. The resulting spaces are no longer Riemann surfaces in the usual sense, but they are quite similar to compact Riemann surfaces. In fact, some of the basic tools of the theory of compact Riemann surfaces are generalized to these spectral curves and illuminate the structure of complete integrability: The eigen bundles define holomorphic line bundles on the spectral curves, which completely determine the potentials. These line bundles may be described by divisors of the same degree as the genus, and these divisors give rise to Darboux coordinates. With the help of a Riemann-Roch Theorem, the isospectral sets (the sets of all potentials corresponding to the same spectral curve) may be identified with open dense subsets of the Jacobian varieties. The real parts of the isospectral sets are infinite dimensional tori, and the group action solves the corresponding nonlinear partial differential equations. Deformations of the spectral curves are in one to one correspondence with holomorphic forms. Serre Duality reproduces the symplectic form.

Author : A Kundu
Publisher : CRC Press
Page : 320 pages
File Size : 42,7 Mb
Release : 2019-04-23
Category : Science
ISBN : 1420034618

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Classical and Quantum Nonlinear Integrable Systems by A Kundu Pdf

Covering both classical and quantum models, nonlinear integrable systems are of considerable theoretical and practical interest, with applications over a wide range of topics, including water waves, pin models, nonlinear optics, correlated electron systems, plasma physics, and reaction-diffusion processes. Comprising one part on classical theories

Author : Albrecht Böttcher,Marinus A. Kaashoek,Amarino Brites Lebre,Antonio, F. dos Santos,Frank-Olme Speck
Publisher : Birkhäuser
Page : 393 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880077

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Singular Integral Operators, Factorization and Applications by Albrecht Böttcher,Marinus A. Kaashoek,Amarino Brites Lebre,Antonio, F. dos Santos,Frank-Olme Speck Pdf

This volume contains the proceedings of the International Workshop on Operator Theory and Applications held at the University of Algarve in Faro, Portugal, September 12-15, in the year 2000. The main topics of the conference were !> Factorization Theory; !> Factorization and Integrable Systems; !> Operator Theoretical Methods in Diffraction Theory; !> Algebraic Techniques in Operator Theory; !> Applications to Mathematical Physics and Related Topics. A total of 94 colleagues from 21 countries participated in the conference. The major part of participants came from Portugal (32), Germany (17), Israel (6), Mexico (6), the Netherlands (5), USA (4) and Austria (4). The others were from Ukraine, Venezuela (3 each), Spain, Sweden (2 each), Algeria, Australia, Belorussia, France, Georgia, Italy, Japan, Kuwait, Russia and Turkey (one of each country). It was the 12th meeting in the framework of the IWOTA conferences which started in 1981 on an initiative of Professors 1. Gohberg (Tel Aviv) and J. W. Helton (San Diego). Up to now, it was the largest conference in the field of Operator Theory in Portugal.

Author : Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita
Publisher : American Mathematical Soc.
Page : 349 pages
File Size : 42,9 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821829387

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Differential Geometry and Integrable Systems by Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita Pdf

Ideas and techniques from the theory of integrable systems are playing an increasingly important role in geometry. Thanks to the development of tools from Lie theory, algebraic geometry, symplectic geometry, and topology, classical problems are investigated more systematically. New problems are also arising in mathematical physics. A major international conference was held at the University of Tokyo in July 2000. It brought together scientists in all of the areas influenced by integrable systems. This book is the first of three collections of expository and research articles. This volume focuses on differential geometry. It is remarkable that many classical objects in surface theory and submanifold theory are described as integrable systems. Having such a description generally reveals previously unnoticed symmetries and can lead to surprisingly explicit solutions.Surfaces of constant curvature in Euclidean space, harmonic maps from surfaces to symmetric spaces, and analogous structures on higher-dimensional manifolds are some of the examples that have broadened the horizons of differential geometry, bringing a rich supply of concrete examples into the theory of integrable systems. Many of the articles in this volume are written by prominent researchers and will serve as introductions to the topics. It is intended for graduate students and researchers interested in integrable systems and their relations to differential geometry, topology, algebraic geometry, and physics. The second volume from this conference, also available from the 'AMS', is ""Integrable Systems, Topology, and Physics, Volume 309"" in the ""Contemporary Mathematics"" series. The forthcoming third volume will be published by the Mathematical Society of Japan and will be available outside of Japan from the 'AMS' in the ""Advanced Studies in Pure Mathematics"" series.

Author : Chudnovsky
Publisher : Routledge
Page : 209 pages
File Size : 52,7 Mb
Release : 2018-10-08
Category : Mathematics
ISBN : 9781351460545

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Classical and Quantum Models and Arithmetic Problems by Chudnovsky Pdf

Here is an unsurpassed resource-important accounts of a variety of dynamic systems topicsrelated to number theory. Twelve distinguished mathematicians present a rare complete analyticsolution of a geodesic quantum problem on a negatively curved surface ... and explicitdetermination of modular function growth near a real point .. . applications of number theoryto dynamical systems and applications of mathematical physics to number theory . ..tributes to the often-unheralded pioneers in the field ... an examination of completely integrableand exactly solvable physical models .. . and much more!Classical and Quantum Models and Arithmetic Problems is certainly a major source of information,advancing the studies of number theorists, algebraists, and mathematical physicistsinterested in complex mathematical properties of quantum field theory, statistical mechanics,and dynamic systems. Moreover, the volume is a superior source of supplementary readingfor graduate-level courses in dynamic systems and application of number theory .

Author : Percy Deift,Luen-Chau Li,Carlos Tomei
Publisher : American Mathematical Soc.
Page : 101 pages
File Size : 51,9 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821825402

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Loop Groups, Discrete Versions of Some Classical Integrable Systems, and Rank 2 Extensions by Percy Deift,Luen-Chau Li,Carlos Tomei Pdf

The theory of classical $R$-matrices provides a unified approach to the understanding of most, if not all, known integrable systems. This work, which is suitable as a graduate textbook in the modern theory of integrable systems, presents an exposition of $R$-matrix theory by means of examples, some old, some new. In particular, the authors construct continuous versions of a variety of discrete systems of the type introduced recently by Moser and Vesclov. In the framework the authors establish, these discrete systems appear as time-one maps of integrable Hamiltonian flows on co-adjoint orbits of appropriate loop groups, which are in turn constructed from more primitive loop groups by means of classical $R$-matrix theory. Examples include the discrete Euler-Arnold top and the billiard ball problem in an elliptical region in $n$ dimensions. Earlier results of Moser on rank 2 extensions of a fixed matrix can be incorporated into this framework, which implies in particular that many well-known integrable systems--such as the Neumann system, periodic Toda, geodesic flow on an ellipsoid, etc.--can also be analyzed by this method.

Author : Sergey Novikov,Igor Krichever,Oleg Ogievetsky,Senya Shlosman
Publisher : American Mathematical Soc.
Page : 516 pages
File Size : 42,9 Mb
Release : 2021-04-12
Category : Education
ISBN : 9781470455910

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Integrability, Quantization, and Geometry: I. Integrable Systems by Sergey Novikov,Igor Krichever,Oleg Ogievetsky,Senya Shlosman Pdf

This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.